In order to replace multi-stage fiber pre-amplification structure in a master oscillator power amplification structure, a grazing incidence slab laser amplifier with small signal and high gain is simulated and studied experimentally. The thermal conversion coefficient of the slab crystal is measured by an axicon structure caused by the linear temperature gradient in the slab. The results show that the thermal conversion coefficient are 0.37 and 0.28 for 0.1 mW and 1 W seed laser extraction, respectively. When the pump light power is 55 W, the maximum temperature rise difference of the slab between two cases is 16 K. Under small signal extraction, the temperature rise in the slab crystal becomes the main constraint on the gain increasing. The laser output power of 1.8 W is obtained when the power of seed laser is 0.1 mW and the pump light power is 50 W. The gain is as high as 43 dB, the horizontal beam quality factor M2x is 1.30 and the vertical beam quality factor M2y is 1.28.